German Patent Application (OS) No. 1,506,473 describes a safety brake which decelerates an elevator when a predetermined speed of rotation of the transmission shaft is exceeded and which is driven via a gear wheel meshing with a rack as guide means. The safety brake comprises a speed limiter in the form of a centrifugal governor with centrifugal weights mounted on the transmission shaft to be decelerated, a brake structure in the form of a bell which surrounds the speed limiter and which is engaged by the centrifugal weights of the speed limiter when a predetermined speed of rotation is exceeded and which is mounted for rotation in a housing, a means for axial displacement of the brake bell, and a means for decelerating the transmission shaft when the brake bell is axially shifted. In such prior art safety brake the centrifugal weights snugly engage the inside of the brake bell to thereby rotate it. The means for axial displacement of the brake bell consists of a spindle with a spindle sleeve secured against rotation which urges the brake bell against a stationary brake member thereby to decelerate it when it is caused to rotate by actuation of the centrifugal brake. Since the braking force is transmitted via the centrifugal weights to the transmission shaft, the operational safety of the safety brake depends on the snug engagement of the centrifugal weights. The edges of the centrifugal weights responsible for the form-locking engagement may partially break away during engagement so that snug fit becomes difficult. Moreover, during the braking operation the braking force constantly increases. For a short stopping distance the braking force therefore must be very high at the end of the braking operation, which puts the elevator guidance and all supporting parts under heavy stress.